Comment, for lack of doc: if a weight is swinging on a string from a point, and if the string can be shortened in the center of the swing, and lengthened on the ends, the weight travels in a figure-8, and gains energy, because the lifting in the center is against greater centrifugal force. This principle can be applied to any undulatory motion. Raise weight perpendicular to the points of greatest curvature, increasing kinetic energy. I suspect almost any undulatory locomotion can be understood that way - fish, birds, kids going uphill on skateboards.
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Mike DunlaveyFeb 17 '12 at 1:32

2 Answers
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Bifins work in a way similar to a fishes tail, with one essential differences. A fishes tail propels the fish equally when moving in either direction, whereas bifins are designed to give a push mainly on the upstroke of the leg and reduce drag on the recovery stroke when the fin moves down. This is because when we walk we push ourselves forward when a foot is on the ground and the leg is moving backwards relative to the body position, So muscles and joints are designed to be efficient at pushing when moving in the backward direction. In particular the knee joint locks when pushing back and then bends when lifted off the ground to move forwards. The design of the fins needs to be optimized to work with similar movements underwater. The fins work best when the legs move up and down in turn so that each fin propels the swimmer while the other is moving back for the next stroke.

During the power stroke the fin moves up at an angle so as to push the water. Fins have ridges on the edges to help direct the flow along the fin so that it comes of the trailing edge rather than the edges during the power stroke. The widening of the fin and the curve of the trailing edge also help keep the water flowing over the fin in a way the optimizes the thrust. These aspects of the shape and design are similar to some fishtails.

One design of fins uses holes near the foot which are angled so as to let the water pass through the fin on the recovery stroke. This is said to reduce drag during the non-propulsive part of the movement. These have been marketed under the trademark named of jetfins. There is controversy about how effective this really is but such fins are popular with scuba divers. The front side of the fin may not have ridges so that the water can also flow off the sides during the recovery stroke.

The size, length and flexibility of fins varies to match the strength of the swimmer and the type of use. A scuba diver needs to be able to control direction and apply a force while moving quite slowly in order to overcome drag of equipment. A speed swimmer may use a longer fin that curves more to work better at speed and possibly also apply some force when moving in both directions. In this case a single monofin can be more efficient.

That sounds like basically the same as a fish propelling itsself with it's caudal fin, though the plane of undulation is vertical instead of horizontal. I doubt there's much difference in the physics. See: